Question

A regular octagon (8-sided polygon) has an area of 690 sq. ft. and a side length of 20feet. Find the length of the apothem to the nearest foot.

Answer 1

Given:

`\begin{gathered} s=\text{side length} \\ s=20\text{ fe}et \\ a=\text{ apothem length} \\ n=\text{ number of sides of a polygon} \\ n=8 \end{gathered}`

Apothem length.

`a=(s)/(2\tan ((180)/(n)))`
`\begin{gathered} a=(20)/(2\tan ((180)/(8))) \\ a=(20)/(2\tan (22.5)) \\ a=(20)/(2*0.4142) \\ a=(20)/(0.828) \\ a=24.142 \end{gathered}`

Length of the apothem is 24.142